Decoding multi-scale stochastic mechanics of soil-rock Mixtures: A DEM-Based investigation

Soil-rock mixtures (SRMs) are heterogeneous geomaterials widely used in geotechnical engineering. Their irregular particle arrangements and complex force chain evolution introduce inherent randomness, complicating reliable prediction. Traditional triaxial tests and simulations typically control macroscale properties such as rock content ( R c ) or porosity, while neglecting particle-scale variability and lacking criteria for sample quantity. This study proposes a framework integrating multiscale discrete element method (DEM) simulations, particle dynamics, and Bootstrap resampling to decode the random nature of SRMs. A comprehensive simulation strategy spans the full parameter space, covering R c = 0–100 %, varied particle shapes, and specimen sizes. Randomized simulations capture variability in spatial particle arrangements and orientations, while new mesoscale indicators link internal disorder to macroscale behavior. Results show that R c controls failure mode transitions: low R c (<30 %) leads to gradual failure via soil matrix shearing, whereas high R c ( ≥ 70 %) causes brittle failure driven by rock rotation and rearrangement, with stress softening exceeding 50 % and dilatancy increasing by 3–4 times. These transitions are governed by force chain evolution, with post-peak softening tied to the collapse of short looped chains and the emergence of long ones in shear zones, showing clear R c -dependence. A strong correlation (coefficient of determination: 0.65–0.90) is found between geometric variability of shear zone thickness and mechanical response dispersion, revealing how particle-scale dynamics propagate to specimen-scale behavior. Based on extensive simulations, we propose practical test guidelines: for R c ≥ 70 %, use 200 mm specimens with 5–11 simulations; for R c = 30–70 %, 175–200 mm with 3–6; and for R c < 30 %, 125–150 mm with 3–4. By treating randomness as an inherent material property rather than experimental noise, this study transforms SRMs into quantifiable systems, providing engineers with physics-based guidelines for slope stability and dam design. • Soil-rock mixtures (SRMs) are defined as quantifiable random systems. • Rock content ( R c ) triggers transition from progressive shear to brittle failure. • Short-chain collapse and long-chain growth govern R c -dependent mechanics. • Macroscale randomness of SRMs emerges from mesoscale particle disorder. • Reliability guidelines specify required specimen sizes and simulation counts.